Fraction Fish and Other Friends

Transcription

1 Fraction Fish and Other Friends MA.A and.4 LESSON FOCUS Building models/diagrams to represent quantities between zero and one. COMPANION ANCHORS LESSONS Equal Parts of a Whole; Halves and Thirds; Fourths MATERIALS Excursions student pages Transparencies TR1 4 Home Connection pages Precut construction-paper circles and squares or construction paper and patterns Paper clips Scissors One zipper bag for each child Ruler denominator eighth equal parts fourth fraction LANGUAGE DEVELOPMENT fraction bar half numerator quarter whole to the square so that one half is covered and ask: What part of the square is red? What part of the square is blue? Write 1 2 on the board. Clip the second blue rectangle so that it covers the remaining half of the square, and ask, Now what part of the square is blue? Prompt children to recognize that the whole square is now blue. Invite a volunteer to take away one of the blue rectangles and ask, Now what part of the square is red? ( 1 ) Invite another child to take away the 2 remaining rectangle. Now what part of the square is red? (the whole square) Have the two children who are each holding a rectangle place them together to make a whole square. Point out that now there are two whole squares and that the blue square has two equal parts. Each part is one half of the whole. Make sure children understand that both parts are equal in size. LESSON OVERVIEW In this lesson, children explore fractions that express equal parts of a whole. They begin by examining and folding area models and identifying how many equal parts comprise the whole. They practice using conventional notation and terms for naming fractions, including, fourths (quarters), and eighths. In closing, each child will build a design using fraction models and record the number of fractional parts used. SETTING THE STAGE Use an area model to express the concepts of whole and half. Prepare a large red construction-paper square and two blue rectangles of equal size that together equal the whole. Hold up the large square and the two rectangles and have children describe them. Show the class that the two blue rectangles are equal in size by placing one on top of the other. Clip one rectangle FOCUS ON LANGUAGE Demonstrate the words used to name parts of fractions. A numerator is the top number in a fraction. It tells how many parts of the whole are being expressed. A denominator is the bottom number in a fraction. It names the number of equal parts into which the whole is divided. A fraction bar is the line that separates the two. BUILDING CONCEPTUAL KNOWLEDGE Explore equal parts of a circle using area models. Explain that a circle can be divided into equal parts. The parts can be named by a fraction. Hold up a large construction-paper circle. Tell children that this is a whole circle. Give children four precut construction-paper circles about 6 inches in diameter, or provide paper and a circle pattern to trace and have children use 143

2 TOPIC 6 Fraction Fish and Other Friends scissors to cut out four circles. Display TR1 on the overhead, allowing only the whole circle and the two half circles to be shown. Use the large paper circle to demonstrate how to fold a circle in the middle so that both are equal. Tell children to fold one of the small circles carefully, making sure that both are the same size. Once you have checked each child s fold, tell children to cut along the fold to create two. Ask children how many equal parts the circle now has. Hold one half of a circle in the air and say: I am holding one of two equal parts. Write the fraction 1 2 on the board. Tell children that the number below the fraction bar, or the denominator, tells how many equal parts together make up the whole. Point to 1 2 on the board and say: The denominator is two because 2 parts make up the whole circle. Tell children that the number above the fraction bar, or the numerator, names a part of a whole. Take a second large paper circle and fold it so that it doesn t have two equal parts. Cut along the fold line. Hold the two pieces together and ask: Is this a whole circle? Then hold up one of the segments and ask: Is this a half circle? Discuss the difference between two parts and two equal parts. FOCUS ON LANGUAGE Use models to demonstrate the meaning of fourths and eighths. Discuss the use of whole, half, and. Explain that fourths are also sometimes called quarters. Ask children if they have ever heard the word quarters used to describe items or objects (four quarters in a dollar, or four quarters of a football game). Discuss how their suggestions are related to the fraction one fourth. Explore fourths using area models. Have children fold and cut a second circle to create two. Display TR1 on the overhead, showing the top two lines of the transparency. Demonstrate how to fold one of the in the middle so that both parts are equal in size. Name Fraction Fish and Other Friends DRAWING FRACTIONS Use a ruler to draw a straight line between the marks. How many parts did you show for each circle? FRACTION PICTURES Use your fraction pieces to make a picture. Glue the pieces to the paper. Tell how many of each sized piece you used. Write the numerator for each fractional value. School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal fourths eighths Use your ruler to show how you folded and cut squares into and fourths. TOPIC 6 Fraction Fish and Other Friends fourths two hundred eleven 211 whole circles. of the circle. 2 of the circle fourths. 4 of the circle eighths two hundred twelve TOPIC 6 Fraction Fish and Other Friends Page 211 Page

3 TOPIC 6 Fraction Fish and Other Friends Ask children to fold each of their in half carefully, making sure that all four quarters are the same size. Once you have checked each child s folds, have children cut along the folds to create four quarters. Ask children how many equal parts this circle has. Hold up one quarter of a circle and say: I am holding one of the four equal parts. Write the fraction 1 4 on the board. Ask children to point to the denominator. Ask: How many equal parts make up the whole? (four equal parts) Point to the numerator and ask: How many of those equal parts am I holding? (one of four equal parts) What fraction of the circle am I holding? (one fourth of the circle) Have children label each quarter circle with the fraction 1 4. Discuss the use of the word quarter as an alternate way to say fourth. Hold up three quarter pieces of a circle and say: I am holding three of the four equal parts. Write the fraction 3 4 on the board. Ask children to point to the denominator, and ask them: How many equal parts make up the whole? (four equal parts) Point to the numerator and ask: How many of those equal parts am I holding? (three of four equal parts) What fraction of the circle am I holding? (three fourths of the circle). Write 2 4 on the board. Challenge children to hold up the pieces of the circle that show two fourths of the whole. Explore eighths using area models. Ask children to cut their third circle into fourths in the same way they cut the second circle. Display the entirety of TR1 on the overhead. Point out that it shows a step-by-step process for cutting a circle in eighths. Demonstrate how to fold one of the fourths in the middle so that both parts are equal in size. Ask children to fold each of their fourths in half carefully, making sure that all eight pieces are the same size. Once you have checked each child s folds, have children cut along the folds to create eight eighths. Ask children how many equal parts this circle has. Hold up one eighth of a circle and say: I am holding one of the eight equal parts. Write the fraction 1 8 on the board. Ask children to point to the denominator and ask: How many equal parts make up the whole? (eight equal parts) Point to the numerator and ask: How many of those equal parts am I holding? (one of eight equal parts) What fraction of the circle am I holding? (one eighth of the circle) Hold up two eighths of a circle and say: I am holding two of the eight equal parts. Write the fraction 2 8 on the board. Ask children to point to the denominator, and ask them: How many equal parts make up the whole? (eight equal parts) Point to the numerator and ask: How many of those equal parts am I holding? (two of eight equal parts) What fraction of the circle am I holding? (two eighths of the circle) Write 3 8, 4 8, 5 8 on the board. Challenge children to hold up the pieces of the circle that show each of the fractions. Then have them show and say the name for the remaining fractions ( 6 8, 7 8, 8 8 ). Point out that 8 8 is a whole because all of the eight parts of the whole are represented. Put all of the pieces (1 whole, 2, 4 fourths, and 8 eighths) in a zipper bag to be used again in Putting It into Action. BUILDING SKILLS AND STRATEGIES Divide diagrams to show area models of, fourths, eighths. Have children turn to Drawing Fractions, page 211. Provide a ruler and demonstrate how to use it to draw a straight line between the marks through the midpoint of the circle. After children have drawn dividing lines on the first circle, ask: How many parts did you show for this circle? When they have bisected the second circle, ask the same question. Point out that any line drawn through the midpoint of a circle will divide the circle into equal. Have children record the number 2 and label each half circle with the fraction 1 2. Repeat this process with the circles marked for division into fourths and eighths. Have children label the parts of the circles. Make sure that children understand that drawing any two lines bisecting a circle won t result in fourths. Some children may find this exercise difficult. Have them return to their paper circles to review the concepts. Provide children with precut paper squares. Follow the same procedure used above with circles to demonstrate how to fold and then cut a square into two and four quarters. Have them use a ruler to draw straight lines to show how the squares on the bottom of their page can be divided into and quarters. Challenge children to invent a way to fold and cut a square into eight equal pieces. 145

4 TOPIC 6 Fraction Fish and Other Friends PUTTING IT INTO ACTION Create patterns using fractional parts of circles. Have children remove from their zipper bags the pieces they cut from different circles in Building Conceptual Knowledge. Have them reconstruct the whole circles using one size part for each circle. They should have a whole circle, a circle showing, one showing fourths, and one showing eighths. Have them set aside the and eighths and use the fourths for the next activity. Display TR2 on the overhead. Have children practice putting the fourths together to make the designs by copying the patterns shown on the overhead. Repeat this activity using the eighths and overhead transparency TR3. Point out that in some cases, to reproduce the pattern, they place the pieces edge to edge, and in others, one piece is placed partially on top of another. Encourage children to invent new patterns and challenge others to reproduce it. Display TR4 on the overhead. Mask all of the creatures other than the elf. Ask children which pieces they can see in the picture. Build the elf together as a class. Ask children how many whole circles they used. (1) How many? (1) How many fourths? (1) How many eighths? (2) pieces,, fourths, and eighths they used. Then ask them to complete the fractions by adding the numerators. Remind children that if the numerator and denominator are the same, the value is one whole. Ask them if any of their pictures used a whole or more than a whole. Display the pictures and allow time for them to be examined and admired. Then describe a picture. For example, say: This picture was created with three fourths and five eighths. Let children hunt for and identify the picture. EXTENSION Repeat the activities in this lesson with squares. Encourage children to find various ways to cut the squares into fractional pieces and to put the pieces together. HOME CONNECTION: Have children share Home Connection, pages with their families. Reveal TR4 in its entirety. Have children work in pairs to create another one of the designs with their combined fraction pieces. Invite partners to show their designs to other pairs and to say how many of each size piece they used to create it. Have children turn to Fraction Pictures, page 212. Allow each child to create and glue down a design using fraction pieces. On the bottom of the page, ask them to fill in the number of whole 146

5 Name Fraction Fish and Other Friends DRAWING FRACTIONS 5Use a ruler to draw a straight line between the marks. How many parts did you show for each circle? School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal. fourths eighths 5Use your ruler to show how you folded and cut squares into and fourths. TOPIC 6 Fraction Fish and Other Friends fourths two hundred eleven 211

6 FRACTION PICTURES 5Use your fraction pieces to make a picture. Glue the pieces to the paper. Tell how many of each sized piece you used. Write the numerator for each fractional value. whole circles. 1 of the circle. 2 1 of the circle fourths. 4 1 of the circle eighths two hundred twelve TOPIC 6 Fraction Fish and Other Friends